Answers
Answer: are there any other pictures or other ways to word it?
Related Questions
A first number plus twice a second number is 8. . Twice the first number plus the second totals 34
Answers
Answer:
20-6Step-by-step explanation:
You want two numbers such that ...
first plus twice the second is 8twice the first plus the second is 34.SetupLet x and y represent the first and second numbers, respectively. Then the given relations can be written as the equations ...
x +2y = 8
2x +y = 34
SolutionSolving the first equation for x gives ...
x = 8 -2y
Using that in the second equation, we have ...
2(8 -2y) +y = 34
16 -3y = 34 . . . . . . eliminate parentheses
-18 = 3y . . . . . . . . add 3y-34
-6 = y . . . . . . . . divide by 3
x = 8 -2(-6) = 8 +12 = 20
The first number is 20, and the second number is -6.
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A 7
th grade class is taking an end-of-year trip to an amusement park. Each student will pay $48
. The cost covers the $22
admission fee, a ticket to the aquatic show, and a ticket to the firework display. The tickets to the aquatic show and fireworks display are the same price.
What is the price of each ticket?
Answers
Answer: $13
Step-by-step explanation:
Let x be the price of each ticket (to the aquatic show and fireworks display).
Then, we know that:
$48 = $22 + 2x
Simplifying this equation, we get:
$48 - $22 = 2x
$26 = 2x
x = $13
Therefore, the price of each ticket is $13.
If c is a nonzero constant such that x^2+cx+9c is equal to the square of a binomial, then what is c?
Answers
Answer:
c = 6.
Step-by-step explanation:
x^2+cx+9 = (x + b)^2 where b is a constant
x^2 + cx + 9 = x^1 + 2bx + b^2
so 2b = c
and b^2 = 9
So b = 3
and c = 2*b = 6
To solve this problem, we will use the fact that the square of a binomial (a+b)^2 is equal to a^2 + 2ab + b^2.
Let's start by assuming that x^2 + cx + 9c is the square of a binomial (a+b)^2. Expanding (a+b)^2 using the formula above, we get:
(a+b)^2 = a^2 + 2ab + b^2
If we compare this to x^2 + cx + 9c, we see that:
a^2 = x^2 (1)
2ab = cx (2)
b^2 = 9c (3)
From (1), we get a = ±√x^2 = ±x.
Substituting a = ±x into (2), we get:
2(±x)b = cx
Simplifying this equation, we get:
b = ±(c/2)
Substituting a = ±x and b = ±(c/2) into (3), we get:
x^2 + (c/2)^2 = 9c
Multiplying both sides by 4, we get:
4x^2 + c^2 = 36c
Rearranging this equation, we get:
4x^2 - 36c + c^2 = 0
This is a quadratic equation in c. Using the quadratic formula, we get:
c = (36 ± √(36^2 - 4(4)(c^2))) / (2(4))
Simplifying this equation, we get:
c = (9 ± √(81 - c^2)) / 2
Since c is nonzero, we can ignore the solution c = 0. Therefore, we have:
c = (9 + √(81 - c^2)) / 2 or c = (9 - √(81 - c^2)) / 2
We can check that both solutions satisfy the original condition that x^2 + cx + 9c is the square of a binomial.
However, we need to ensure that the square root in each solution is real, which means that 81 - c^2 ≥ 0.
For the first solution, we have:
81 - c^2 ≥ 0
c^2 ≤ 81
|c| ≤ 9
Therefore, the first solution is valid for c such that -9 ≤ c ≤ 9.
For the second solution, we have:
81 - c^2 ≥ 0
c^2 ≤ 81
|c| ≥ 9
However, we already know that c is nonzero, so |c| > 0. Therefore, the second solution is not valid for any value of c.
Therefore, the only valid solution is:
c = (9 + √(81 - c^2)) / 2, for -9 ≤ c ≤ 9.
I hope this helps! Let me know if you have any questions.
If x^2 + cx + 9c is equal to the square of a binomial, then it can be written in the form (x + A)^2, where A is a constant. Expanding the square of the binomial, we get:
(x + A)^2 = x^2 + 2Ax + A^2
Comparing this with the given expression, x^2 + cx + 9c, we can deduce the following:
2A = c and A^2 = 9c
We are asked to find the value of c. Using the first equation (2A = c), we can substitute c in the second equation:
A^2 = 9(2A)
A^2 = 18A
Since A is nonzero, we can divide both sides by A:
A = 18
Now, using the first equation, we can find the value of c:
c = 2A
c = 2(18)
c = 36
Therefore, the value of c is 36.
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plsss helpppp 6 grade math
Answers
Straight angles equals 180 so 180-60
2.50
Right angles equal 90 degrees so 90-40
Anybody know how to do this?
Answers
The point which is a solution to the system y = x + 7 and y = 11 - x is: 2. (2, 9).
The value of b in the second equation must be: 1. 10.
The x-coordinate of the solution to the system is: 4. x = -2.
The y-coordinate of the solution is: 4. y = 4.
The point (2, 5) would not be a solution to this equation: 4. 2x + 4y = 12
How to determine the solution to the system of equations?In this scenario and exercise, you are required to determine the solution to the given system of equations as follows;
y = x + 7
y = 11 - x
By using the substitution method, we have the following:
x + 7 = 11 - x
2x = 4
x = 4/2 = 2.
y = x + 7 = 2 + 7 = 9.
Question 2:Next, we would determine the value of b as follows;
x = 1
y = 3x + 5 = 3(1) + 5 = 8
y = -2x + b
b = y + 2x = 8 + 2(1) = 10.
Question 3:For the x-coordinate of the solution to the system, we have:
y = 4x + 7
x + y = -3
-3 - x = 4x + 7
5x = -10
x = -10/5 = -2.
Question 4:For the y-coordinate of the solution, we have:
x + 3 = -2x + 6
3x = 3
x = 1
y = x + 3 = 1 + 3 = 4
Question 5:2x + 4y = 12
2(2) + 4(5) = 12
4 + 20 = 12
24 = 12 (False).
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Suppose someone claims the average delivery time for u.s. packages to be delivered during december is 2 days. you believe it takes longer than that. you conduct a hypothesis test; what are your hypotheses?
Answers
The null hypothesis (H0) is that the average delivery time for U.S. packages during December is 2 days, while the alternative hypothesis (Ha) is that the average delivery time is longer than 2 days.
Based on your question, you want to test if the average delivery time for U.S. packages in December is longer than 2 days. In this hypothesis test, you would have the following hypotheses:
Null Hypothesis (H0): The average delivery time for U.S. packages in December is 2 days.
Alternative Hypothesis (H1): The average delivery time for U.S. packages in December is greater than 2 days.
Thus, H0: μ ≤ 2 (where μ is the population mean delivery time)
Ha: μ > 2
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A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 5 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 5 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.
What is the area of the tile shown?
53 cm2
45.5 cm2
42.5 cm2
36.5 cm2
Answers
What is the volume of the solid figure?
A rectangular prism on top of another longer rectangular prism. The top prism measures 5 inches by 5 inches by 5 inches. The bottom prism measures 20 inches by 5 inches by 5 inches.
Answers
Answer:
The volume of the solid figure is 625 cubic inches.
Step-by-step explanation:
The volume of a rectangular prism is found by multiplying its length, width, and height.
For the top prism, the volume is:
5 inches x 5 inches x 5 inches = 125 cubic inches
For the bottom prism, the volume is:
20 inches x 5 inches x 5 inches = 500 cubic inches
To find the total volume of the solid figure, we need to add the volumes of the two prisms together:
Total volume = 125 cubic inches + 500 cubic inches = 625 cubic inches
Therefore, the volume of the solid figure is 625 cubic inches.
Regenerate response
in the standard normal distribution, what is the proportion of values between negative infinity and 1 z-score?
Answers
Thus, the proportion of values between negative infinity and 1 z-score in the standard normal distribution is about 84.13%.
In the standard normal distribution, the proportion of values between negative infinity and 1 z-score can be determined using the cumulative distribution function (CDF) of the normal distribution.
The standard normal distribution, also known as the Z-distribution, has a mean (µ) of 0 and a standard deviation (σ) of 1. The proportion of values between negative infinity and any z-score corresponds to the area under the curve of the standard normal distribution up to that z-score.To find the proportion of values between negative infinity and 1 z-score, you can consult a Z-table or use a statistical calculator or software that provides the CDF for the standard normal distribution. The CDF value for a z-score of 1 is approximately 0.8413.Therefore, the proportion of values between negative infinity and 1 z-score in the standard normal distribution is about 84.13%. This means that 84.13% of the data points lie to the left of a z-score of 1 in a standard normal distribution.Know more about the cumulative distribution function (CDF)
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a company receives customer satisfaction ratings on a scale from 0 to 10, inclusive. on the first six surveys that the company received, the average (arithmetic mean) of the ratings was 7.7. what is the least rating the company can receive on the seventh survey and still be able to have an average of at least 8 for the first 10 surveys? (round to the nearest tenth.)
Answers
The least amount of ratings the particular company can receive is 3 on the seventh survey and still be eligible to have an average of at least 8 for the first 10 surveys.
Here we have to implement basic algebraic application
Let us consider x as the the least rating the company can get on the seventh survey.
The average of the first six surveys is 7.7, so their total score is 6 × 7.7 = 46.2.
The average of at least 8 for the first ten surveys, their total score should be at least 80.
So for the first ten surveys, their total score should be
80 = (46.2 + x + y)/10
Here
y = score for survey 8 and survey 9.
Evaluating for y
y = (80 - 46.2 - x × 2)/2
= (33.8 - x)/2.
As each survey rating is an integer between 0 and 10 inclusive, we need to find the smallest integer value of x that makes y ≥ 0
Then, (33.8 - x)/2 >= 0.
Multiplying both sides by 2
33.8 - x >= 0
Subtracting 33.8 from both sides
-x >= -33.8
Multiplying both sides by -1
x <= 33.8
Hence, the smallest integer value of x that makes y ≥0 is x = 3.
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Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day. A bird with these tendencies is released from an island that is 5 km from the nearest point B on a straight shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. Points B and D are 13 km apart. (a) In general, if it takes 1. 4 times as much energy to fly over water as land, to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area?(b) Let W and L denote the energy (in joules) per kilometer flown over water and land, respectively. What would a large value of the ratio W/L mean in terms of the bird's flight? What would a small value mean? Determine the ratio W/L corresponding to the minimum expenditure of energy. (c) What should the value of W/L be in order for the bird to fly directly to its nesting area D? What should the value of W/L be for the bird to fly to B and then along the shore to D?(d) If the ornithologists observe that birds of a certain species reach the shore at a point 4 km from B, how many times more energy does it take a bird to fly over water than land?
Answers
The bird should fly to a point on the shoreline that is 4km from B to minimize total energy expenditure. A large W/L ratio means it's more efficient to fly over land, while a small ratio means it's more efficient to fly over water. The minimum ratio is 2.834. The W/L ratio should be 1 for the bird to fly directly to D, and 0 for the bird to fly to B and then along the shore to D. It takes a bird 1.4 times more energy to fly over water than land.
To minimize the total energy expended in returning to its nesting area, the bird should fly to the point on the shoreline that is 4 km from B. This can be found using the principle of least action, which states that the bird will choose the path that minimizes the integral of the energy expended along the path.
A large value of the ratio W/L would mean that it takes significantly more energy to fly over water than over land. A small value of the ratio would mean that there is not much difference in energy expenditure between flying over water and over land. The ratio W/L corresponding to the minimum expenditure of energy can be found using the same principle of least action as in part (a).
we are asked to determine the ratio W/L corresponding to the minimum expenditure of energy. Let x be the distance from B to C, and let y be the distance from C to D along the shoreline. Then the total energy expended in returning to its nesting area is given by
E(x, y) = L(13 - x - y) + W(√(25 - x²)) + W(√(y² + (13 - x)²))
To minimize E(x, y), we take partial derivatives with respect to x and y and set them equal to zero
dE/dx = L + Wx/√(25 - x²) - Wy/√(y² + (13 - x)²) = 0
dE/dy = L - Wy/√(y² + (13 - x)²) = 0
Solving for x and y, we get
x = 5√((W/L)/(1.4(W/L) - 1))
y = 13 - x - 5√((W/L)/(1.4(W/L) - 1))
The ratio W/L corresponding to the minimum expenditure of energy is obtained by substituting these values into the expression for E(x, y) and simplifying
W/L = 2.5(1.4 + √(1.96 + 4/25))/(4.9 - √(1.96 + 4/25))
W/L ≈ 2.834
Therefore, the ratio W/L corresponding to the minimum expenditure of energy is approximately 2.834.
To fly directly to its nesting area D, the value of W/L should be equal to 1. To fly to B and then along the shore to D, the value of W/L should be equal to 0.
If birds of a certain species reach the shore at a point 4 km from B, it takes 1.4 times more energy for the bird to fly over water than over land. This can be found by comparing the energy required to fly directly from the island to the point on the shoreline that is 4 km from B (which is entirely over water) to the energy required to fly along the shoreline from that point to D (which is entirely over land).
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A student says the histogram is skewed right with an outlier and intervals of 5. Is the student correct? If not explain
Answers
The student is not correct because there are intervals of 4 and the histogram is relatively symmetric.
Why is the student wrong ?The histogram is not skewed right, but instead appears to be faintly symmetrical; the frequency of points commence from a count of 0, proceeding to pulsate up to 4 and then progressively meander downward from there to 3.
No apparent outlier can be seen in the provided histogram data; this refers to any data point that disagreeably differs from the remainder of datasets. In this occurrence, no numbers stand out significantly deviantly from the rest.
The intervals used in the histogram are not five units wide, but four units wide instead.
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Graphing quadratic equations
Answers
A graph of the given quadratic equation is shown below.
The axis of symmetry is equal to 3.
The vertex is equal to (3, -1).
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function y = x² - 6x + 8 is positive 1, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -1.
In conclusion, the axis of symmetry is 3 while the vertex is given by the ordered pair (3, -1).
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Ixl please help please
Answers
The ordering of the topics from broader to narrowest are given as follows:
The influence of popular media on elections.The influence of television programs on elections.The influence of televised debates on elections.What are broad and narrow topics?Broad topics are topics that affect a larger amount of the population than narrower topics affect.
In the context of this problem, we have that the television is a subset of the popular media, hence the popular media is broader than the television.
Televised debates are one program on the television, that is, it is a subset of the television, hence television programs are broader than television debated.
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a raffle for a charity fund-raiser is being planned. each of 2000 raffle tickets will be sold for $1.00 . the holders of 32 winning tickets will each win a prize. the table shows the prize values and the number of prizes for each value. prize value number of prizes $25 20 $50 10 $300 2 the random variable w represents the value of the prize won for a single ticket minus the cost of the ticket. what is the expected value of w ?
Answers
The expected value 'w' for the total raffle tickets sold for $1.00 with other conditions is equal to $0.784.
Number of raffle tickets sold for $1.00 = 2000
Expected value of w is ,
= Expected value of the prize won - cost of a single ticket $1.00
The probability of winning a $25 prize is
= 20/2000
= 0.01.
The expected value of winning this prize is equal to
= (25 - 1) × 0.01
= 0.24
The probability of winning a $50 prize is
= 10/2000
= 0.005.
The expected value of winning this prize is equal to
= (50 - 1) × 0.005
= 0.245
The probability of winning a $300 prize is
= 2/2000
= 0.001.
The expected value of winning this prize is,
= (300 - 1) × 0.001
= 0.299
This implies,
The expected value of w is equal to
= 0.24 + 0.245 + 0.299
= 0.784
Therefore, the expected value of winning a prize minus the cost of the ticket is $0.784.
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14+5x -11= 7x+3-2x
what is it
Answers
The equation "14 + 5x -11 = 7x + 3 - 2x" has infinitely many solutions, so any value of "x" will satisfy the equation.
In order to solve for "x" in the equation "14 + 5x - 11 = 7x + 3 - 2x", we need to simplify the expression by combining like terms:
14 + 5x - 11 = 7x + 3 - 2x
Simplifying the LHS,
We get,
3 + 5x = 7x + 3 - 2x
Simplifying the RHS,
We get,
3 + 5x = 5x + 3
Subtracting 5x from both sides,
We get,
3 = 3
The equation simplifies to 3 = 3, which is always true.
This means that the equation has infinitely many solutions and that any value of "x" will satisfy the equation.
Therefore, there is no unique value of "x" that can be found from the equation.
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The given question is incomplete, the complete question is
Find the value of "x" in the expression "14+5x -11= 7x+3-2x".
What value of X makes the equation 33x=11 true
Answers
Answer:
x = 1/3
Step-by-step explanation:
To solve this equation for x, divide each side by 33.
33x/33 = 11/33
x = 1/3
Answer:
x=3
Step-by-step explanation:
The value of x that makes the equation true is 3.
What is an equation?
An equation is a statement that equates to two expressions.
The given equation is:
Divide both sides by 11
So, the required value of x=3.
a measure of meaningfulness that expresses the difference between the experimental and control group in standard deviation units is the
Answers
The measure you're referring to is called "Cohen's d." It expresses the difference between the experimental and control group in standard deviation units, providing an indicator of effect size and meaningfulness in a study.
The measure of meaningfulness that expresses the difference between the experimental and control group in standard deviation units is the effect size. Effect size is typically calculated by dividing the difference between the means of the two groups by the standard deviation of the control group. It is a useful tool for comparing the effectiveness of different interventions or treatments, as it allows researchers to assess the magnitude of the difference between the groups beyond just statistical significance.
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In the diagram below, the dimensions of the large rectangle are (3x-1) by (3x+7) units. The Demi sound of the cut-out rectangle are x by 2x+5 units. Write a simplified expression for the area of the shaded region, in square units.
Answers
The expression that represents the area of shaded region is expressed as:
How to Write the Expression for the Area of the Shaded Region?The area of the shaded region = area of larger rectangle - area of smaller rectangle.
Area of a rectangle = length * width
Area of shaded region = [(3x + 7)(3x - 1)] - [(2x + 5)(x)]
Area of shaded region = (9x² + 18x - 7) - (2x² + 5x)
Open the bracket:
9x² + 18x - 7 - 2x² - 5x
Combine like terms:
9x² - 2x² + 18x - 5x - 7
Area of shaded region = 7x² + 13x - 7
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Questions from Page 45 in Dale Seymour Publications' Developing Skills in Algebra Book B (adding all of this info in case someone needs to keyword it at some point)
4.] The side of one square is five times that of another square. The difference in the areas of the two squares is 96. Find the sum of the areas of the two squares.
6.] The second side of a triangle is four more than the first side, and the third side is five more than the second. If the product of the first and third sides is added to the product of the second and third sides, the result is 124 more than twice the square of the first side. Find the perimeter of the triangle.
7.] A concrete walk 5 m wide is built around a grass court. The length of the court is 12 m more than its width. The area of the walk is 560 m^2. Find the dimensions of the grass court.
Answers
The sum of the areas of the two squares = 104
The perimeter of the triangle is 27.67
How to solve for the area1. We have 5x)² - x² = 96
next wer have to solve for x
25x² - x² = 96
x = 2
x² = 2² = 4
5x)² = 10² = 100
sum of the areas = 4 + 100 = 104
2. b = a + 4
c = b + 5
ac + bc = 2a^2 + 124
substitute b and c from the relationships:
When we simplify we have 18a = 88
a = 44/9
b = a + 4 = 44/9 + 4 = 80/9
c = b + 5 = 80/9 + 5 = 125/9
perimeter = a + b + c:
= 44/9 + 80/9 + 125/9
= 249/9 = 27.67
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Graph the given data set and describe what kind of model best describes the data. Then write a function that models
the data.
x y
-2,-1
-1,-3
0,-1
1,2
2,7
Answers
The graph of the data set is in the image at the end, and it can be modeled by the quadratic:
y = 2*(x + 1)² - 3
How to find a function that models the data?Here we have the table:
x y
-2, -1
-1, -3
0, -1
1, 2
2, 7
The graph of it can be seen in the image at the end, there we can see that this seems to be a quadratic function
At the graph we also can see that (-1, -3) is te vertex, then if the leading coefficient is a, we can write the quadratic equation as:
y = a*(x + 1)² - 3
And we know that the equation passes throug (0, -1), replacing that we will get.
-1 = a*(0 + 1)² - 3
-1 = a - 3
-1 + 3 = a
2 = a
The function is:
y = 2*(x + 1)² - 3
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9.a. Find the H.C.F. of: [3] x² - y² - 2yz - z² and y² - z² - 2zx - x²
Answers
Answer:
We can rewrite the given expressions as:
(3x² - y² - 2yz - z²) and (y² - z² - 2zx - x²)
To find the H.C.F., we can use the Euclidean algorithm. We start by dividing the first expression by the second expression:
(3x² - y² - 2yz - z²) ÷ (y² - z² - 2zx - x²)
Using long division or synthetic division, we get:
(3x² - y² - 2yz - z²) = (3x + y + z)(x - y + z) + 2y(x - z)
Therefore, the remainder is 2y(x - z). We can now divide the second expression by this remainder:
(y² - z² - 2zx - x²) ÷ 2y(x - z)
Using long division or synthetic division, we get:
(y² - z² - 2zx - x²) = -x(x - y + z) + z(x - y + z)
Therefore, the remainder is z(x - y + z).
Since the second remainder is not zero, we need to continue with the algorithm. Now we divide the remainder 2y(x - z) by the remainder z(x - y + z):
2y(x - z) ÷ z(x - y + z)
Using long division or synthetic division, we get:
2y(x - z) = 2y(x - y + z) - 2y²
Therefore, the remainder is -2y². Now we divide the previous remainder z(x - y + z) by this new remainder:
z(x - y + z) ÷ (-2y²)
Using long division or synthetic division, we get:
z(x - y + z) = -1(-2y²) + z²
Therefore, the H.C.F. of the original expressions is the absolute value of the last remainder, which is |-2y²| = 2y².
Therefore, the H.C.F. of (3x² - y² - 2yz - z²) and (y² - z² - 2zx - x²) is 2y².
If we want to decrease the type ii error in a hypothesis test while maintaining type i error at its current level we should:_______
Answers
To decrease the type II error in a hypothesis test while maintaining the type I error at its current level, we need to increase the sample size.
What is detailed explaination of the given answer?Type I error shows when we reject a null hypothesis which is actually true. Type II error shows when we fail to reject a null hypothesis which is actually false.
Increasing the sample size can decrease the probability of making a Type II error, as it increases the power of the hypothesis test. Probability of correctly rejecting a false null hypothesis is called power.
By increasing the sample size, we can increase the power of the test while maintaining the significance level (and thus the type I error) at its current level.
This means that we will be less likely to miss a true effect (i.e., lower the probability of making a Type II error) while still controlling the probability of false positives (i.e., Type I error) at the desired level.
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solve for x: 4(x−3) = 96
Answers
4(x−3) = 96
x=27
-12 + 12 + 4x = 96 + 12
Combine like terms: -12 + 12 = 0 0 + 4x = 96 + 12
4x = 96 + 12
Combine like terms: 96 + 12 = 108
4x = 108
Divide each side by '4'.
x = 27
(5 points) how many ways are there to distribute seven distinct apples and six distinct pears to three distinct people such that each person has at least one pear?
Answers
There are 77,910 ways to distribute the seven distinct apples and six distinct pears to three distinct people such that each person has at least one pear.
How to use the principle of inclusion-exclusion to solve this problem?We can use the principle of inclusion-exclusion to solve this problem. Let A be the set of all possible ways to distribute the apples and pears without any restrictions, and let B, C, and D be the sets of ways to distribute the apples and pears such that person 1, person 2, and person 3, respectively, does not receive a pear.
We can compute |A|, the total number of ways to distribute the apples and pears, as follows:
|A| = (7 + 6) choose 3 = 78 choose 3 = 82,251
To compute |B|, we can first choose 6 pears to give to persons 2 and 3 (since person 1 cannot receive a pear). This can be done in (6 choose 2) = 15 ways. Then, we can distribute the remaining 7 apples and 1 pear to the three people in any way, which can be done in (8 choose 1) * (6 choose 2) = 84 ways. Therefore, |B| = 15 * 84 = 1,260.
Similarly, |C| = |B| and |D| = |B|, since the problem is symmetric with respect to the three people.
To compute |B intersection C|, we can choose 6 pears to give to person 3 (since persons 1 and 2 cannot receive a pear). This can be done in (6 choose 1) = 6 ways. Then, we can distribute the remaining 7 apples and 2 pears to persons 1 and 2 in any way, which can be done in (9 choose 2) = 36 ways. Therefore, |B intersection C| = 6 * 36 = 216.
Similarly, |B intersection D| = |C intersection D| = |B intersection C|, since the problem is symmetric with respect to the three people.
To compute |B intersection C intersection D|, we can simply distribute the 7 apples and 3 pears among the three people in any way, which can be done in (13 choose 3) = 286 ways.
Therefore, by the principle of inclusion-exclusion, the number of ways to distribute the apples and pears such that each person has at least one pear is:
|A intersection complement(B union C union D)| = |A| - |B union C union D| = |A| - (|B| + |C| + |D| - |B intersection C| - |B intersection D| - |C intersection D| + |B intersection C intersection D|) = 82,251 - (3 * 1,260 - 3 * 216 + 286) = 77,910.
Therefore, there are 77,910 ways to distribute the seven distinct apples and six distinct pears to three distinct people such that each person has at least one pear.
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What would the Volume and Surface area of a pentagonal pyramid be if the Apothem is 3 square root 2 and the height is 3
Answers
The volume of the Pentagonal pyramid is 8.25 units² and surface area is 12.2 units²
What is volume of a pyramid?A Pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces.
The volume of of a pyramid is expressed as;
V = 1/3 b × h
where b is the area of the base
Area of the base = 1/2 nsa
where s is the side length and n is the number of sides and a is the apothem.
side length = apothem × 2tan(180/n)
= √3/2 × 2tan36
= √3 × tan36
= 1.26m
Therefore,
A = 1/2( 5 × 1.26 × √3/2)
A = 1/2 ( 5.5)
A = 2.75 units²
Volume of the pyramid = 2.75 × 3
= 8.25 units²
Area of a face = 1/2bh
= 1/2 × 1.26 × 3
= 3.78/2
= 1.88 units²
Total surface area = 1.88 × 5
= 9.45 units² + 2.75units²
= 12.2 units²
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Find the length of a side of a square if its area is: 40 inches
Answers
Answer:
Side = 6.3245 inches
Step-by-step explanation:
Area of square = side²
40 in² = side²
√(40 in²) = √(side²)
6.3245 in = side
You have the chance to purchase a car for $6,250.
You must put 10% down and finance the balance at 6% for 36 months. Sales tax is 8.25 %.
You have no trade in.
What are the monthly payments?
Answers
The monthly payments after the down payment are $186.58 per month.
What are the monthly payments?We will first calculate amount of the down payment which is:
= 10% * 6,250.
= $625.
So, the financed amount for the purchase will be:
= $6,250 - $625
= $5,625.
We will now calculate the amount of sales tax where tax rate is 8.25%, this give us:
= $6,250 * 8.25%
= $515.63.
The total amount financed including sales tax is:
= $5,625 + $515.63
= $6,140.63.
To calculate the monthly payments, we can use the formula M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
M = $6,140.63* [ 0.005(1 + 0.005)^36 ] / [ (1 + 0.005)^36 – 1 ]
M = $6,140.63* 0.03042193745
M = $186.58
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Edward is making his special punch for the Starry Night homecoming dance.
There is a proportional relationship between the number of cans of peach juice concentrate in a punch bowl, x, and the corresponding number of bottles of lemon-lime soda, y.
x (cans of peach juice concentrate) y (bottles of lemon-lime soda)
2 6
3 9
4 12
5 15
Write an equation for the relationship between x and y. Simplify any fractions.
y=
Answers
The equation of the line is written as y = (2/3)x + (14/3).
The equation of a line is a mathematical representation of the relationship between each point's x and y coordinates along a straight line.
Y = mx + b, where m is the line's slope and b is its y-intercept, is its mathematical formula (the point where the line intersects the y-axis). This equation allows us to rapidly calculate the y-coordinate of a point given its x-coordinate.
The equation of the line can be written as,
y = mx + c
The slope of the line is,
m = ( y₂ - y₁) / (x₂ - x₁)
m = ( 6 - 2 ) / ( 9-3 )
m = 2/3
The y-intercept is calculated as,
y = 2/3x + c
6 = (2/3) x 2 + c
c = 14/3
The equation of the line is,
y = 2/3x + 14/3
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2. A trolley car track rises vertically 40 feet over a horizontal distance of 630 feet. What is the angle of
elevation of the track?
Answers
Step-by-step explanation:
For a right triangle
tan Φ = opposite leg / adjacent leg
tan Φ = 40 / 630
Φ = arctan (40/630) = 3.6 degrees
